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Properties

Label 242.6
Level 242
Weight 6
Dimension 2975
Nonzero newspaces 4
Sturm bound 21780
Trace bound 1

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Defining parameters

Level: \( N \) = \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(21780\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(242))\).

Total New Old
Modular forms 9235 2975 6260
Cusp forms 8915 2975 5940
Eisenstein series 320 0 320

Trace form

\( 2975 q - 40 q^{6} + 1180 q^{7} - 2200 q^{9} + O(q^{10}) \) \( 2975 q - 40 q^{6} + 1180 q^{7} - 2200 q^{9} - 2000 q^{10} - 890 q^{11} - 320 q^{12} + 2020 q^{13} + 4400 q^{14} + 12980 q^{15} + 1600 q^{17} - 9640 q^{18} - 4470 q^{19} - 17640 q^{21} - 35400 q^{23} - 640 q^{24} + 38720 q^{25} + 33440 q^{26} + 66990 q^{27} + 6080 q^{28} + 4280 q^{29} - 33360 q^{30} - 67980 q^{31} - 10240 q^{32} - 55495 q^{33} - 30560 q^{34} - 8120 q^{35} + 1760 q^{36} + 31240 q^{37} + 81840 q^{38} + 112460 q^{39} + 39680 q^{40} + 79160 q^{41} - 53680 q^{42} - 107460 q^{43} - 5680 q^{44} - 44500 q^{45} + 104800 q^{46} + 133760 q^{47} + 96800 q^{49} - 14240 q^{50} - 90890 q^{51} - 83840 q^{52} - 185020 q^{53} - 233280 q^{54} - 44950 q^{55} + 63150 q^{57} - 66880 q^{58} + 130790 q^{59} + 63360 q^{60} - 77780 q^{61} + 42480 q^{62} + 184240 q^{63} + 229480 q^{65} + 286160 q^{66} - 31700 q^{67} + 25600 q^{68} - 190740 q^{69} - 251680 q^{70} + 79200 q^{71} - 79360 q^{72} - 39120 q^{73} - 184160 q^{74} - 382910 q^{75} - 115520 q^{76} + 164700 q^{77} - 413120 q^{78} - 179540 q^{79} - 56320 q^{80} - 1340790 q^{81} - 245080 q^{82} - 226570 q^{83} + 355840 q^{84} + 1031580 q^{85} + 1135640 q^{86} + 1874200 q^{87} + 95360 q^{88} + 922760 q^{89} + 1020720 q^{90} - 21560 q^{91} + 10560 q^{92} - 1083940 q^{93} - 906880 q^{94} - 1439020 q^{95} + 84370 q^{97} - 864360 q^{98} - 265450 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(242))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
242.6.a \(\chi_{242}(1, \cdot)\) 242.6.a.a 1 1
242.6.a.b 1
242.6.a.c 1
242.6.a.d 1
242.6.a.e 1
242.6.a.f 2
242.6.a.g 2
242.6.a.h 2
242.6.a.i 3
242.6.a.j 3
242.6.a.k 4
242.6.a.l 4
242.6.a.m 4
242.6.a.n 4
242.6.a.o 6
242.6.a.p 6
242.6.c \(\chi_{242}(3, \cdot)\) n/a 180 4
242.6.e \(\chi_{242}(23, \cdot)\) n/a 550 10
242.6.g \(\chi_{242}(5, \cdot)\) n/a 2200 40

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)